Quasi-optimality of an adaptive finite element method for an optimal control problem

Abstract

We prove quasi-optimality of an adaptive finite element algorithm for a model problem of optimal control including control constraints. The quasi-optimility expresses the fact that the decrease of error with respect to the number of mesh cells is optimal up to a constant. The considered algorithm is based on an adaptive marking strategy which compares a standard residual-type a posteriori error estimator with a data approximation term in each step of the algorithm in order to adapt the marking of cells. © 2011 Institute of Mathematics.